Method, device, computer program and computer program product for determining a representation of a signal

ABSTRACT

A method for determining a representation (y) of a signal (s) comprise selecting a predetermined number (m) of row vectors (v 1 , . . . , vm) from a predetermined measurement matrix (M). The predetermined measurement matrix (M) is predetermined dependent on a product of a predetermined Hadamard matrix or generalized Hadamard matrix (H) and a predetermined representation matrix(B). The predetermined representation matrix (B) represents a predetermined basis for the signal(s). The method further comprises determining a respective inner product of the signal (s) and each of the predetermined number (m) of selected row vectors (v 1 , . . . , vm) resulting in a predetermined number (m) of measurements (y 1 , . . . , ym) forming the representation (y) of the signal (s).

CROSS-REFERENCE TO RELATED APPLICATION

This application claims priority from PCT Application No.PCT/IB2009/054807, filed on Oct. 29, 2009, the entire contents of whichare incorporated herein by reference. This application also claimspriority under 35 U.S.C. §119 from European Patent Application No.08105710.1 filed Oct. 30, 2008, the entire contents of which are alsoincorporated herein by reference.

TECHNICAL FIELD

The present invention relates to a method, a device, a computer programand a computer program product for determining a representation of asignal and in particular a compressed representation of a signal.

BACKGROUND OF THE INVENTION

Traditional capture and processing of analogue signals consists of twosteps: sample, then compress. If the signal is bandlimited, then sampleat a little over the Nyquist frequency, namely at twice the frequencyrange. Lossy compression, for example JPEG for an image, then throwsaway lots of redundant information. Compressive sampling is a new andpromising method to simultaneously sample and compress a signal.

In E. J. Candès and M. Wakin: “An introduction to compressive sampling”,IEEE Signal Processing Magazine, 25:21-30, March 2008, a method forcompressive sampling is described. A signal, which is sparse under agiven basis, is sampled incoherently under a measurement basis.Measurements are taken uniformly at random. A number of measurements ismuch smaller than a length of the signal.

It is a challenge to provide a method, a device, a computer program anda computer program product for determining a representation of a signalthat is simple and that allows for an efficient representation of thesignal.

SUMMARY OF THE INVENTION

A method for determining a representation (y) of a signal (s) includesselecting a predetermined number (m) of row vectors (v1, . . . , vm)from a predetermined measurement matrix (M). The predeterminedmeasurement matrix (M) being predetermined dependent on a product of apredetermined Hadamard matrix or generalized Hadamard matrix (H) and apredetermined representation matrix (B), the predeterminedrepresentation matrix (B) representing a predetermined basis for thesignal (s) and determining a respective inner product of the signal (s)and each of the predetermined number (m) of selected row vectors (v1, .. . , vm) resulting in a predetermined number (m) of measurements (y1, .. . , ym) forming the representation (y) of the signal (s).

In another aspect, a device for determining a representation (y) of asignal (s) includes at least one processing unit (CPU), at least onememory unit (MEM), at least one signal source (SRC) being coupled to theat least one CPU and at least one signal processing unit (SPU). The atleast one CPU or at least one SPU (i) selects a predetermined number (m)of row vectors (v1, . . . , vm) from a predetermined measurement matrix(M), the predetermined measurement matrix (M) being predetermineddependent on a product of a predetermined Hadamard matrix or generalizedHadamard matrix (H) and a predetermined representation matrix (B), thepredetermined representation matrix (B) representing a predeterminedbasis for the signal (s) and (ii) determines a respective inner productof the signal (s) and each of the predetermined number (m) of selectedrow vectors (v1, . . . , vm) resulting in a predetermined number (m) ofmeasurements (y1, . . . , ym) forming the representation (y) of thesignal (s).

The advantage is that by using the predetermined measurement matrix thatis predetermined dependent on the product of the predetermined Hadamardmatrix or generalized Hadamard matrix and the predeterminedrepresentation matrix, the predetermined measurement matrix is maximallyincoherent with respect to the predetermined representation matrix. Thisenables the predetermined number of measurements to be predeterminedsmaller than compared to using another measurement matrix withoutmaximal incoherence with respect to the predetermined representationmatrix. The representation of the signal can thus be efficient.

According to another aspect of the invention, a method for determining arepresentation of a signal is provided. The method includes determininga first transform dependent on the signal by multiplying a predeterminedrepresentation matrix representing a predetermined basis for the signalwith the signal or by applying a first transform algorithm based on thepredetermined basis for the signal to the signal. The method furtherincludes determining a second transform dependent on the first transformby multiplying a predetermined Hadamard matrix or generalized Hadamardmatrix with the first transform or by applying as a second transformalgorithm a Hadamard transform or fast Hadamard transform to the firsttransform. The method further includes selecting a predetermined numberof measurements from the second transform. The predetermined number ofmeasurements form the representation of the signal.

According to yet another aspect of the invention, a device fordetermining a representation (y) of a signal (s) includes at least oneprocessing unit (CPU), at least one memory unit (MEM), at least onesignal source (SRC) being coupled to the at least one CPU and at leastone signal processing unit (SPU), where the at least one CPU or at leastone SPU (i) determines a first transform (b) dependent on the signal (s)by multiplying a predetermined representation matrix (B) representing apredetermined basis for the signal (s) with the signal (s) or byapplying a first transform algorithm (transf(s,B)) based on thepredetermined basis for the signal (s) to the signal (s), (ii)determines a second transform (h) dependent on the first transform (b)by multiplying a predetermined Hadamard matrix or generalized Hadamardmatrix (H) with the first transform (b) or by applying as a secondtransform algorithm (transf(b,H)) a Hadamard transform or fast Hadamardtransform to the first transform (b) and (iii) selects a predeterminednumber (m) of measurements (y1, . . . , ym) forming the representation(y) of the signal (s) from the second transform (h).

The advantage is that by determining the first transform based on thepredetermined basis for the signal and by determining the secondtransform based on the predetermined Hadamard matrix or generalizedHadamard matrix or the Hadamard transform or fast Hadamard transform thepredetermined number of measurements are taken with respect to a basisthat is maximally incoherent with respect to the predetermined basis forthe signal. This enables the predetermined number of measurements to bepredetermined smaller than compared to using another measurement basiswithout maximal incoherence with respect to the predetermined basis forthe signal. The representation of the signal can thus be efficient.Further, the method is simple. By this, the device, the computer programand the computer program product can also be simple.

BRIEF DESCRIPTION OF THE DRAWINGS

The invention and its embodiments will be more fully appreciated byreference to the following detailed description of presently preferredbut nonetheless illustrative embodiments in accordance with the presentinvention when taken in conjunction with the accompanying drawings.

The figures are illustrating:

FIG. 1, a first flow chart of a first embodiment of a method fordetermining a representation of a signal,

FIG. 2, a second flow chart of a second embodiment of the method fordetermining the representation of the signal,

FIG. 3, an example for a predetermined representation matrix, apredetermined Hadamard matrix and a predetermined measurement matrix and

FIG. 4, a device for determining the representation of the signal.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

The term “predetermined” means in the context of this application thatthe corresponding entity can be determined outside the described method,that is, the entity is predetermined with respect to the describedmethod but is not necessarily a constant. For example, the term“predetermined number” can thus include that the number is determineddependent on the signal and can thus be different for different signals.

FIG. 1 shows a first flow chart of a first embodiment of a method and acorresponding computer program for determining a representation y of asignal s of a length n. The method relates to a signal processing schemecalled “compressive sampling” or “compressed sensing”. The method beginsin a step S1. A step S2 may be provided for choosing or determiningand/or providing a predetermined representation matrix B and/or apredetermined Hadamard matrix or generalized Hadamard matrix H and/or apredetermined number m. For a specific application, these may be given,but they may also be determined or chosen, for example, dependent onproperties of the signal s. For example, the predetermined number m maybe determined dependent on the signal s and may thus be different fordifferent signals s, that is, the predetermined number m may bedetermined adaptively based on the signal s.

The predetermined representation matrix B represents a predeterminedbasis for the signal s. Preferably, the predetermined representationmatrix B is a unitary n×n matrix. Preferably, the signal s is sparse orapproximately sparse under the predetermined basis. Particularly, thesignal s is k-sparse or approximately k-sparse under the predeterminedbasis with a sparsity k that is smaller than the length n of the signals and that preferably is much smaller than the length n of the signal s.The signal s has a k-sparse expansion under the predetermined basis ifall but the sparsity k of its values are zero. The signal s has anapproximately k-sparse expansion under the predetermined basis if allbut the sparsity k of its values have a magnitude of less than apredetermined threshold. This predetermined threshold may bepredetermined application dependent. The predetermined thresholdgenerally is predetermined such that the loss of information due toignoring values below the predetermined threshold is acceptable withregard to the application. Preferably, most but a few values of theexpansion of the signal under the predetermined basis are zero or have amagnitude of less than the predetermined threshold. Preferably, thesparsity k amounts to less than ten percent of the length n of thesignal s and further preferably amounts to less than five percent of thelength n of the signal s. The signal s may then be compressedeffectively. The predetermined representation matrix B preferably is notan identity matrix, that is, a product of any Hadamard matrix orgeneralized Hadamard matrix H and the predetermined representationmatrix B preferably always differs from the Hadamard matrix orgeneralized Hadamard matrix H used in the calculation of the product.The same applies to a transform corresponding to the predeterminedrepresentation matrix B, for example a first transform b. An output ofthis transform preferably always differs from its input.

The predetermined number m preferably is predetermined to be smallerthan the length n of the signal s and is preferably predetermined to bemuch smaller than the length n of the signal s. Preferably, thepredetermined number m is predetermined dependent on the sparsity k,that is, the smaller the sparsity k the smaller the predetermined numberm and vice versa. As a rule of thumb the predetermined number m may bepredetermined to amount to about four times the sparsity k. However, thepredetermined number m may be predetermined to be smaller or greaterthan four times the sparsity k. The predetermined number m may bepredetermined dependent on a reconstruction algorithm used forreconstructing the signal s from a predetermined number m ofmeasurements y1, . . . , ym that form the representation y of the signals and/or dependent on requirements with respect to the application.

Generally, a generalized Hadamard matrix is defined as a n×n matrixsatisfying H.H*=nI and with all its entries being roots of unity. Inthis context, H* represents a conjugate transpose of the generalizedHadamard matrix H and I represents an identity matrix. A complex numberw is called a r^(th) root of unity if w^(r)=1. Generally, a Hadamardmatrix is a special case of the generalized Hadamard matrix with all itsentries being real values, that is +1 or −1. Generally, a generalizedHadamard matrix exists for all lengths n of the signal s. Further, it ishypothesized that a Hadamard matrix exists for the length n of thesignal s being 2 or a multiple of 4. For the length n being a power oftwo the predetermined Hadamard matrix H may be easily constructed with aSylvester construction for which also a fast implementation exists.Alternatively, a Paley construction may be used when the length n of thesignal s amounts to q+1 with q being any prime power congruent to 1 or 3modulo 4, that is, q=p¹ for some positive integer 1 and prime p and q=1(mod 4) or q=3 (mod 4). The predetermined generalized Hadamard matrix Hmay for example be a Fourier matrix with elements w^(ij), with rows iand columns j=0, . . . , n−1, where the complex w=cos (2π/n)+i·sin(2π/n) is a i·j-root of unity. However, preferably, the predeterminedgeneralized Hadamard matrix H is not a Fourier matrix if thepredetermined representation matrix B is the identity matrix.

In a step S3 a a predetermined measurement matrix M is provided. Thepredetermined measurement matrix M represents a predeterminedmeasurement basis for taking the predetermined number m of measurementsy1, . . . , ym that form the representation y of the signal s. Thepredetermined measurement matrix M is predetermined dependent on thepredetermined Hadamard matrix or generalized Hadamard matrix H and thepredetermined representation matrix B. Particularly, as shown as a stepS3 b, the predetermined measurement matrix M is predetermined dependenton a product of the predetermined Hadamard matrix or generalizedHadamard matrix H and the predetermined representation matrix B. Bythis, the predetermined measurement matrix M is maximally incoherentwith respect to the predetermined representation matrix B. This holdsfor any predetermined representation matrix B. This allows for theminimal predetermined number m of measurements y1, . . . , ym and thusfor the representation y of the signal s being very efficient.Generally, if the predetermined measurement matrix M is a unitary n×nmatrix, the predetermined measurement matrix M is maximally incoherentto another unitary n×n matrix, that is the predetermined representationmatrix B, if and only if sqrt(n)·B·M^(T) is a generalized Hadamardmatrix, with sqrt(n) representing a square root of the length n of thesignal s and M^(T) representing a transpose of the predeterminedmeasurement matrix M. A coherence between the predeterminedrepresentation matrix B and the predetermined measurement matrix M maybe defined as μ(B,M)=sqrt(n)·max |<uj,vi>| for 1≦i, j≦n with rows i, j,that is, the coherence is a maximum absolute value of all inner productsof row vectors uj of the predetermined representation matrix B and rowvectors vi of the predetermined measurement matrix M. In other words,the coherence measures the largest correlation between any two rowvectors uj, vi of the predetermined representation matrix B andpredetermined measurement matrix M. The maximal incoherence then isachieved when the coherence is smallest.

A step S4 may be provided to provide the signal s. In a step S5, apredetermined number m of row vectors v1, . . . , vm of thepredetermined measurement matrix M are selected from all available rowvectors vi of the predetermined measurement matrix M. In a step S6, aninner product of the signal s and each of the predetermined number m ofthe row vectors v1, . . . , vm is respectively determined. Each of theseinner products forms one of the predetermined number m of measurementsy1, . . . , ym that form the representation y of the signal s. Becausethe predetermined number m preferably is smaller and particularly muchsmaller than the length n of the signal s, the representation y of thesignal s generally is a compressed representation y of the signal s. Themethod ends with a step S7.

The selection of the predetermined number m of the row vectors v1, . . ., vm of the predetermined measurement matrix M may be performed randomlyand preferably uniformly at random. However, the selection mayalternatively be performed differently, for example dependent onrequirements of the reconstruction algorithm.

FIG. 2 shows a second flow chart of a second embodiment of a method anda corresponding computer program for determining the representation y ofthe signal s of the length n. This second embodiment essentially isequivalent to the first embodiment. A difference is that thepredetermined measurement matrix M is not used directly and that thepredetermined representation matrix B and the predetermined Hadamardmatrix or generalized Hadamard matrix H or a respective transformalgorithm are applied separately one after the other. The method startswith a step S10. A step S11 corresponds to the step S2. A step S12corresponds to the step S4.

In a step S13 the first transform b is determined. Two alternatives forthis are presented in FIG. 2. In a first alternative, the firsttransform b is determined dependent on the signal s by multiplying thepredetermined representation matrix B and the signal s. In a secondalternative, the first transform b is determined dependent on the signals by applying a first transform algorithm transf(s,B) that is based onthe predetermined representation matrix B to the signal s. For example,the first transform algorithm transf(s,B) may comprise a discrete cosinetrans-form or a wavelet transform, particularly a fast wavelettransform. However, another first transform algorithm transf(s,B) may beselected. The first and the second alternative are equivalent, but thesecond alternative may be preferred because of the existence of fastimplementations, in software as well as in hardware.

In a step S14 a second transform h is determined. Two alternatives forthis are presented in FIG. 2. In a first alternative, the secondtransform h is determined dependent on the first transform b bymultiplying the predetermined Hadamard matrix or generalized Hadamardmatrix H and the first transform b. In a second alternative, the secondtransform h is determined dependent on the first transform b by applyinga second transform algorithm transf(b,H) that is based on thepredetermined Hadamard matrix or generalized Hadamard matrix H to thefirst transform b. For example, the second transform algorithmtransf(b,H) may comprise a Hadamard transform, a fast Hadamardtransform, a discrete Fourier transform or a fast Fourier transform.However, another second transform algorithm transf(b,H) may be selected.The first and the second alternative are equivalent, but the secondalternative may be preferred because of the existence of fastimplementations, in software as well as in hardware.

In steps S13 and S14 the first alternative of step S13 may be combinedwith the first or the second alternative of step S14. Similarly, thesecond alternative of step S14 may be combined with the first or thesecond alternative of step S14.

In a step S15 the predetermined number m of measurements y1, . . . , ymare selected from the second transform h. The selection of thepredetermined number m of the measurements y1, . . . , ym of the secondtransform h may be performed randomly and preferably uniformly atrandom. However, the selection may alternatively be performeddifferently, for example dependent on requirements of the reconstructionalgorithm.

The methods described with reference to FIG. 1 and FIG. 2 may beimplemented as a computer program comprising program instructions thatcan be performed by a computer. A device DEV may comprise a computer forperforming the program instructions of the computer program. Thecomputer program may alternatively be part of an operating system or ofa basic input/output system of the computer system. A computer readablemedium may be provided embodying the program instructions executable bydevice DEV or the computer system. The computer readable medium may forexample be a CD-ROM, a flash memory card, a hard disc or any othersuitable computer readable medium. However, the methods described withreference to FIG. 1 and FIG. 2 may also be implemented in hardware, forexample as a signal processing unit SPU specifically designed or adaptedto perform the method.

FIG. 3 shows an example of the predetermined representation matrix B,the predetermined Hadamard matrix H and the resulting predeterminedmeasurement matrix M for the length n of the signal s being equal to 4.In this example, the predetermined representation matrix B ispredetermined as a 4×4 Haar matrix. The row vectors vi of thepredetermined measurement matrix M are each shown within a dashed box.The predetermined measurement matrix M is maximally incoherent withrespect to the predetermined representation matrix B. The predeterminedrepresentation matrix B and/or the predetermined Hadamard matrix orgeneralized Hadamard matrix H may alternatively be predetermineddifferently. Generally, the length n of the signal s will be larger than4 in most practical cases.

FIG. 4 shows an example of the device DEV. The device DEV may compriseat least one processing unit CPU and at least one memory unit MEM. Thecomputer program comprising the program instructions of the method maybe loaded into or stored in the memory unit MEM and executed by theprocessing unit CPU. Additionally or alternatively, the signalprocessing unit SPU may be provided for performing the method. At leastone signal source SRC is coupled with the processing unit CPU or signalprocessing unit SPU for providing the signal s. The at least one signalsource SRC may be located external to the device DEV or within thedevice DEV and may comprise a sensor. The device DEV preferably alsocomprises at least one input/output unit IO. Two or more than twodevices DEV may be provided and may be coupled for communication overtheir respective input/output units IO. For example, at least one of thedevices DEV determines the representation y for at least one signal sand transmits this representation y over the input/output unit IO toanother of the devices DEV, for example a main or central device DEV,which receives representations y of signals s from at least one deviceDEV. The compressed representation y of the signal s may be transmittedvery efficiently compared to the signal s itself. The representation yof the signal s may additionally or alternatively to the transmitting bestored very efficiently, for example in the at least one memory unitMEM.

In one embodiment, the at least one signal source SRC may be locatedwithin the at least one processing unit CPU and, for example, may bedesigned as a counter. The values of the respective counter, that is thesignal s, for example, may be used for a performance monitoring of therespective processing unit CPU and/or device DEV. Compressive samplingmay be used for efficient gathering of performance information in amulticore system, that is a system with at least two processing coresper processing unit CPU or with at least two processing units CPU withat least one processing core. Modern processing units CPU containmultiple interacting parts making predicting an actual average of clockcycles per instruction for an execution of a particular piece of codedifficult to achieve. This has led to the introduction of an additionalunit to the processing unit CPU, a performance monitor unit that samplesa performance of the rest of the processing unit CPU. Modern performancemonitor units may contain hundreds of counters for indicating bus usage,caches misses, page faults, branch misses etc, as well as complex logicfor determining which of the many pipelined instruction and predictedbranches actually causes the counter to be increased. The performancemonitor units on the distinct processing units CPU need to supplyinformation to a task scheduler. Also, the logic of the performancemonitor unit must be kept simple so as to reduce the amount of the corethey occupy, that the software that extracts data from them must notconsume too many cycles and the distribution of the data must not usetoo much memory bandwidth, particularly because the data must begathered and processed on some centralized task scheduler running on oneof the processing units CPU. One would expect data from the performancemonitor unit to be heavily structured, as the behavior of threads in arecent pass is likely to resemble a present pass. Hence it should becompressible. Compression would be difficult to achieve using standardscompression techniques without increasing the amount of storage on theperformance monitor unit and introducing delays inappropriate with theneeds of task scheduling. If the nature of the signal s is known it ispossible to sample only the most important aspects of it to get animmediately compressed representation y of the signal s. The averageclock cycles per instruction of the respective processing unit CPU, forexample, represents the average number of cycles over some time periodrequired to execute an instruction. Although the actually average clockcycles per instruction is discrete the rate at which it changes is somuch faster than any realistic sampling period that it can be consideredas a continuous function of time. Compressive sampling may be used todetermine the compressed representation y of this actually average clockcycles per instruction as the signal s allowing for a simple performancemonitor unit and low requirements for storing and bandwidth.

Another application deals with processing data handled in a streamingfashion, for example in streaming databases etc., and performing queriesin these. This can be a daunting operation when there are huge amountsof data at stake. This is a problem that arises, for example, whenhandling network data information, where a typical problem is to returna list of “heavy-hitters”, the top flows responsible for a large amountof the traffic. Another important area is the financial markets such asstorage and analysis of stock and FX rates. In any streaming databasesystem there is the data gathering—the what and how to keepsomething—and the query mechanism—searching through what has beengathered. Compressive sampling, or variations thereof, is a promisingtechnique for determining the what to keep and how to search.

Compressive sampling may further have many imaging applications, forexample in magnetic resonance imaging, or short: MRI, and general camerasensor devices, or applications in audio processing. Use of compressivesampling may thus enable development of new cameras, medical imagedevices, security scanners or audio devices comprising new algorithmsfor recording and sampling audio. Further applications may be possiblewith respect to analogue I/O, in communication systems and networkingand in particular sensor networks. Other applications may also bepossible. Use of compressive sampling may also enable a reduction inpower consumption of devices DEV, particularly because sampling may beperformed in a computational efficient manner yet with an optimallyminimal amount of samples needed.

Although the embodiments of the present invention have been describedhereinabove, the present invention is not limited to the foregoingembodiments. Moreover, the effects described in the embodiments of thepresent invention are merely enumerated examples of the most preferableeffects made by the present invention and the effects of the presentinvention are not limited to those described in the embodiments orexamples of the present invention.

We claim:
 1. A method for determining a representation (y) of a signal(s), comprising: selecting, with a processing unit, a predeterminednumber (m) of row vectors (v1, . . . , vm) from a predeterminedmeasurement matrix (M), the predetermined measurement matrix (M) beingpredetermined dependent on a product of a predetermined Hadamard matrixor generalized Hadamard matrix (H) and a predetermined representationmatrix (B), the predetermined representation matrix (B) representing apredetermined basis for the signal (s); and determining, with theprocessing unit, a respective inner product of the signal (s) and eachof the predetermined number (m) of selected row vectors (v1, . . . , vm)resulting in a predetermined number (m) of measurements (y1, . . . , ym)forming the representation (y) of the signal (s).
 2. The methodaccording to claim 1, wherein a Fourier matrix is used as thegeneralized Hadamard matrix (H).
 3. The method according to claim 1,wherein the selection of the predetermined number (m) of the row vectors(v1, . . . , vm) comprises selecting the predetermined number (m) of therow vectors (v1, . . . , vm) uniformly at random from all row vectors(vi) of the predetermined measurement matrix (M).
 4. The methodaccording to claim 1, wherein the predetermined representation matrix(B) or predetermined basis for the signal (s) is being selected suchthat the signal (s) is k-sparse or with respect to a predeterminedthreshold approximately k-sparse under the predetermined basis for thesignal (s) with a sparsity (k) being smaller than a length (n) of thesignal (s).
 5. A non-transitory computer readable storage mediumtangibly embodying a computer readable program code having computerreadable instructions which when implemented, cause a computer to carryout the steps of the method according to claim
 1. 6. A method fordetermining a representation (y) of a signal (s), comprising:determining, with a processing unit, a first transform (b) dependent onthe signal (s) by multiplying a predetermined representation matrix (B)representing a predetermined basis for the signal (s) with the signal(s) or by applying a first transform algorithm (transf(s,B)) based onthe predetermined basis for the signal (s) to the signal (s);determining, with the processing unit, a second transform (h) dependenton the first transform (b) by multiplying a predetermined Hadamardmatrix or generalized Hadamard matrix (H) with the first transform (b)or by applying as a second transform algorithm (transf(b,H)) a Hadamardtransform or fast Hadamard transform to the first transform (b); andselecting, with the processing unit, a predetermined number (m) ofmeasurements (y1, . . . , ym) forming the representation (y) of thesignal (s) from the second transform (h).
 7. The method according toclaim 6, wherein a Fourier matrix is used as the generalized Hadamardmatrix (H).
 8. The method according to claim 6, wherein the selection ofthe measurements (y1, . . . , ym) comprises selecting the measurements(y1, . . . , ym), from all elements of the second transform (h).
 9. Themethod according to claim 6, wherein the predetermined representationmatrix (B) or predetermined basis for the signal (s) is being selectedsuch that the signal (s) is k-sparse or with respect to a predeterminedthreshold approximately k-sparse under the predetermined basis for thesignal (s) with a sparsity (k) being smaller than a length (n) of thesignal (s).
 10. A non-transitory computer readable storage mediumtangibly embodying a computer readable program code having computerreadable instructions which when implemented, cause a computer to carryout the steps of the method according to claim
 6. 11. A device fordetermining a representation (y) of a signal (s) comprising: at leastone processing unit (CPU); at least one memory unit (MEM); at least onesignal source (SRC) being coupled to said at least one CPU; and at leastone signal processing unit (SPU); wherein said at least one CPU or atleast one SPU (i) selects a predetermined number (m) of row vectors (v1,. . . , vm) from a predetermined measurement matrix (M), thepredetermined measurement matrix (M) being predetermined dependent on aproduct of a predetermined Hadamard matrix or generalized Hadamardmatrix (H) and a predetermined representation matrix (B), thepredetermined representation matrix (B) representing a predeterminedbasis for the signal (s), and (ii) determines a respective inner productof the signal (s) and each of the predetermined number (m) of selectedrow vectors (v1, . . . , vm) resulting in a predetermined number (m) ofmeasurements (yl, . . . , ym) forming the representation (y) of thesignal (s).
 12. The device according to claim 11, wherein the CPU andSPU operate simultaneously.
 13. The device according to claim 11,wherein the CPU and SPU operate sequentially with respect to each other.14. The device according to claim 11, further comprising at least oneinput/output unit.
 15. A device for determining a representation (y) ofa signal (s) comprising: at least one processing unit (CPU); at leastone memory unit (MEM); at least one signal source (SRC) being coupled tosaid at least one CPU; and at least one signal processing unit (SPU);wherein said at least one CPU or at least one SPU (i) determines a firsttransform (b) dependent on the signal (s) by multiplying a predeterminedrepresentation matrix (B) representing a predetermined basis for thesignal (s) with the signal (s) or by applying a first transformalgorithm (transf(s,B)) based on the predetermined basis for the signal(s) to the signal (s), (ii) determines a second transform (h) dependenton the first transform (b) by multiplying a predetermined Hadamardmatrix or generalized Hadamard matrix (H) with the first transform (b)or by applying as a second transform algorithm (transf(b,H)) a Hadamardtransform or fast Hadamard transform to the first transform (b) and(iii) selects a predetermined number (m) of measurements (yl, . . . ,ym) forming the representation (y) of the signal (s) from the secondtransform (h).
 16. The device according to claim 15, wherein the CPU andSPU operate simultaneously.
 17. The device according to claim 15,wherein the CPU and SPU operate sequentially with respect to each other.18. The device according to claim 15, further comprising at least oneinput/output unit.